On higher buckling transitions in supercoiled DNA

Statistical mechanical model for a closed loop plectoneme with weak helix specific forces

We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and average structure of a plectoneme. Notably, due to their chiral nature, helix structure dependent forces break the symmetry between left and right handed supercoiling. The theoretical approach, presented here, also provides a systematic way of enforcing the topological constraint of closed loop supercoiling in the variational approximation. At large plectoneme lengths, by considering correlation functions in an expansion in terms of the spatial mean twist density about its thermally averaged value, it can be argued that topological constraint may be approximated by replacing twist and writhe by their thermal averages. A Lagrange multiplier, containing the sum of average twist and writhe, can be added to the free energy to conveniently inforce this result. The average writhe can be calculated through the thermal average of the Gauss' integral in the variational approximation. Furthermore, this approach allows for a possible way to calculate finite size corrections due to the topological constraint. Using interaction energy terms from the mean-field Kornyshev-Leikin theory, for parameter values that correspond to weak helix dependent forces, we calculate the free energy, fluctuation magnitudes and mean geometric parameters for the plectoneme. We see a slight asymmetry, where interestingly, left handed supercoils have a looser structure than right handed ones, although with a lower free energy, unlike what the previous ground state calculations would suggest.

Nucleosome conformational flexibility and implications for chromatin dynamics

The active role of chromatin in the regulation of gene activity seems to imply a conformational flexibility of the basic chromatin structural unit, the nucleosome. This review is devoted to our recent results pertaining to this subject, using an original approach based on the topology of single particles reconstituted on DNA minicircles, combined with their theoretical simulation. Three types of chromatin particles have been studied so far: a subnucleosome, that is, the (H3-H4)(2) histone tetramer-containing particle, now known as the tetrasome; the nucleosome; and the linker histone H5/H1-bearing nucleosome (the chromatosome). All the particles were found to exist in two to three conformational states, which differ by their topological and mechanical properties. Our approach unveiled the molecular mechanisms of nucleosome conformational dynamics and will help to understand its functional relevance. A most surprising conclusion of the work was perhaps that DNA overall flexibility increases considerably upon particle formation, which might indeed be a requirement of genome function.

From the sequence to the superstructural properties of DNAs

A theoretical model for predicting intrinsic and induced DNA superstructures as well as their thermodynamic properties is presented. Intrinsic sequence-dependent superstructures are evaluated by integrating local deviations from the canonical B-DNA of the different dinucleotide steps. Induced superstructures are obtained by adopting the principle of minimum deformation free energy, evaluated in the Fourier space, in the framework of first-order elasticity. Finally dinucleotide stacking energies and melting temperatures are considered to account for local flexibility. In fact the two scales are strongly correlated. The model works very satisfactorily in predicting the sequence-dependent effects on the DNA experimental behavior, such as the gel electrophoresis retardation, the writhe transitions in topologically constrained domains, the thermodynamic constants of circularization reactions as well as the nucleosome thermodynamic stability constants.

Approach to Monte Carlo calculation of the buckling of supercoiled DNA loops

The short supercoiled circular DNA molecules are shown to be glassy systems and canonical Metropolis Monte Carlo simulations of the systems tend to get stuck in local metastable energy basins. A Monte Carlo algorithm is developed to alleviate the problem of "ergodicity breaking" of the glassy systems, in which the Markov process is driven by an explicitly analytic weight factor with enhanced probability in both low- and high-energy regions. To characterize the degree of puckering of the supercoiled DNA loops, a different quantity of aplanarity is introduced as the shortest principal axis of configurational ellipsoid of DNA. With the suggested Monte Carlo method, the quantitative correlation between supercoiling degree and buckling of DNA is attained. With supercoiling stress increasing, the conformational transition from a circle to mono-, diplo-, or triple interwound superhelical structure will take place in a successive but decreasingly abrupt mode.

Nucleosome dynamics. II. High flexibility of nucleosome entering and exiting DNAs to positive crossing. An ethidium bromide fluorescence study of mononucleosomes on DNA minicircles

H2A-H2B exchange with the intranuclear histone pool upon chromatin transcription in vivo is generally viewed as being triggered by the DNA positive supercoiling wave pushed by the elongating polymerase. This notion was tested here by investigating a potential release of H2A-H2B by ethidium bromide-induced positive supercoiling in the loop of mononucleosomes reconstituted on DNA minicircles. The results of gel electrophoresis, fluorescence titration and electron microscopy showed that such a positive supercoiling was not able to release H2A-H2B, nor to unfold the nucleosome to any detectable extent. The reason appeared to be the ease with which the loop could undergo a positive crossing, a surprising observation in view of the DNA left-handed wrapping around the octamer. Moreover, the influence of histone acetylation suggested that such loop flexibility to positive crossing is mediated by histone N-terminal tails which, by interacting with entering and exiting DNAs, reduce their electrostatic repulsion. These conclusions are confirmed and extended in the accompanying article through relaxation with topoisomerase I.

Configurational transitions in Fourier series-represented DNA supercoils

A new Fourier series representation of supercoiled DNA is employed in Langevin dynamics simulations to study large-scale configurational motions of intermediate-length chains. The polymer is modeled as an ideal elastic rod subject to long-range van der Waals' interactions. The van der Waals' term prevents the self-contact of distant chain segments and also mimics attractive forces thought to stabilize the association of closely spaced charged rods. The finite Fourier series-derived polymer formulation is an alternative to the piecewise B-spline curves used in past work to describe the motion of smoothly deformed supercoiled DNA in terms of a limited number of independent variables. This study focuses on two large-scale configurational events: the interconversion between circular and figure-8 forms at a relatively low level of supercoiling, and the transformation between branched and interwound structures at a higher superhelical density.

Nucleosomes as topological rheostats

Induction of transcription in eukaryotic promoters is accompanied by removal or remodeling of nucleosomes. Given that this process causes release of torsional stress, the question is asked relative to its fate and to its effects on local DNA conformation. Is it dispersed by free rotation through surrounding nucleosomes or does it stay locally to be used in the modulation or activation of the transcription machinery? The results of the calculations relative to the onset of writhing suggest that the free energy made available by removal of nucleosomes is in the range of values that corresponds to the transition linking difference, thus pointing to a possible regulatory mechanism for the local use of free energy in promoters.

The effect of ionic conditions on the conformations of supercoiled DNA. I. Sedimentation analysis

We studied the conformations of supercoiled DNA as a function of superhelicity and ionic conditions by determining its sedimentation coefficient both experimentally and by calculation. To cancel out unknown parameters from both calculations and experiments, we determined the ratio of the sedimentation coefficient, s, to that of open circular DNA, s(oc). Calculations of the sedimentation coefficient were based on direct solution of the Burgers-Oseen problem for an equilibrium set of DNA conformations generated for each condition by the Metropolis Monte Carlo procedure. There were no adjustable parameters in the Monte Carlo simulations because all three parameters of the DNA model used, bending and torsional elasticity of DNA and DNA effective diameter specifying electrostatic interactions, were known from independent data. The good agreement between measured and calculated values of s/s(oc) allowed us to interpret the sedimentation results in terms of DNA conformations, with particular emphasis on the marked effect of ionic conditions. As NaCl concentration decreases, s/s(oc) increases because the superhelix becomes less regular and more compact. In the presence of just 10 mM MgCl(2), supercoiled DNA adopts essentially the same set of conformations as in moderate to high concentrations of NaCl. Our simulations showed that s is a strong function of the superhelix branching frequency. At near physiological ionic conditions, there are about four branches in the 7 kb DNA molecule used in this work. We found no indication of superhelix collapse in any ionic conditions even remotely approaching physiological ones. For all ionic conditions studied, we conclude that the electrostatic interaction of DNA segments specified by the DNA effective diameter is the primary determinant of supercoiled DNA conformations.

Buckling transitions in superhelical DNA: dependence on the elastic constants and DNA size

Buckling transitions in superhelical DNA are sudden changes in shape that accompany a smooth variation in a key parameter, such as superhelical density. Here we explore the dependence of these transitions on the elastic constants for bending and twisting. A and C, important characteristics of DNA's bending and twisting persistence lengths. The large range we explore extends to other elastic materials with self-contact interactions, modeled here by a Debye-Hückel electrostatic potential. Our collective description of DNA shapes and energies over a wide range of p = A/C reveals a dramatic dependence of DNA shape and associated configurational transitions on p: transitions are sharp for large p but masked for small p. In particular, at small p, a nonplanar circular family emerges, in agreement with Jülicher's recent analytical predictions: a continuum of forms (and associated writhing numbers) is also observed. The relevance of these buckling transitions to DNA in solution is examined through studies of size dependence and thermal effects. Buckling transitions smooth considerably as size increases, and this can be explained in part by the lower curvature in larger plasmids. This trend suggests that buckling transitions should not be detectable for isolated (i.e., unbound) DNA plasmids of biological interest, except possibly for very large p. Buckling phenomena would nonetheless be relevant for small DNA loops, particularly for higher values of p, and might have a role in regulatory mechanisms: a small change in superhelical stress could lead to a large configurational change. Writhe distributions as a function of p, generated by Langevin dynamics simulations, reveal the importance of thermal fluctuations. Each distribution range (and multipeaked shape) can be interpreted by our buckling profiles. Significantly, the distributions for moderate to high superhelical densities are most sensitive to p, isolating different distribution patterns. If this effect could be captured experimentally for small plasmids by currently available imaging techniques, such results suggest a slightly different experimental procedure for estimating the torsional stiffness of supercoiled DNA than considered to date.

Molecular modeling of closed circular DNA thermodynamic ensembles

Many modeling studies of supercoiled DNA are based on equilibrium structures from theoretical calculations or energy minimization. Since closed circular DNAs are flexible, it is possible that errors are introduced by calculating properties from a single minimum energy structure, rather than from a complete thermodynamic ensemble. We have investigated this question using molecular dynamics simulations on a low resolution molecular mechanics model in which each base pair is represented by three points (a plane). This allows the inclusion of sequence-dependent variations of tip, inclination, and twist. Three kinds of sequences were tested: (1) homogeneous DNA, in which all base pairs have the helicoidal parameters of an ideal, average B-DNA; (2) random sequence DNA; and (3) curved DNA. We examined the rate of convergence of various structural parameters. Convergence for most of these is slowest for homogeneous sequences, more rapid for random sequences, and most rapid for curved sequences. The most slowly converging parameter is the antipodes profile. In a plasmid with N base pairs (bp), the antipodes distance is the distance dij from base pair i to base pair j halfway around the plasmid, j = i + N/2. The antipodes profile at time tau is a plot of dij over the range i = 1, N/2. In a homogeneous plasmid, convergence requires that the antipodes profile averaged over time must be flat. Even in the small plasmids examined here, the average properties of the ensembles were found to differ from those of static equilibrium structures. These effects will be even more dramatic for larger plasmids. Further, average and dynamic properties are affected by both plasmid size and sequence.

Molecular dynamics simulations of small DNA plasmids: effects of sequence and supercoiling on intramolecular motions

Small (600 base pair) DNA plasmids were modeled with a simplified representation (3DNA) and the intramolecular motions were studied using molecular mechanics and molecular dynamics techniques. The model is detailed enough to incorporate sequence effects. At the same time, it is simple enough to allow long molecular dynamics simulations. The simulations revealed that large-scale slithering occurs in a homogeneous sequence. In a heterogeneous sequence, containing numerous small intrinsic curves, the centers of the curves are preferentially positioned at the tips of loops. With more curves than loop tips (two in unbranched supercoiled DNA), the heterogeneous sequence plasmid slithers short distances to reposition other curves into the loop tips. However, the DNA is immobilized most of the time, with the loop tips positioned over a few favored curve centers. Branching or looping also appears in the heterogeneous sequence as a new method of repositioning the loop tips. Instead of a smooth progression of increasing writhing with increasing linking difference, theoretical studies have predicted that there is a threshold between unwrithed and writhed DNA at a linking difference between one and two. This has previously been observed in simulations of static structures and is demonstrated here for dynamic homogeneous closed DNA. Such an abrupt transition is not found in the heterogeneous sequence in both the static and dynamic cases.

Calculations of nucleic acid conformations

The present computational power and sophistication of theoretical approaches to nucleic acid structural investigation are sufficient for the realization of static and dynamic models that correlate accurately with current crystallographic, NMR and solution-probing structural data, and consequently are able to provide valuable insights and predictions for a variety of nucleic acid conformational families. In molecular dynamics simulations, the year 1995 was marked by the foray of fast Ewald methods, an accomplishment resulting from several years' work in the search for an adequate treatment of the electrostatic long-range forces so primordial in nucleic acid behavior. In very large systems, and particularly in the RNA-folding field, techniques originating from artificial intelligence research, like constraint satisfaction programming or genetic algorithms, have established their utility and potential.

Simulating DNA at low resolution

The past year has witnessed the development of several new mathematical approaches to analyzing the structure of double-helical DNA and to incorporating the sequence-dependent features of the chain in computer simulations of long polymers. Of special interest in this respect are the local and global structural changes induced by the binding of various proteins to DNA, ranging from subtle bending, untwisting and sliding motions at the base-pair level to the apparent organization of supercoiled structure in chains that are thousands residues long. The computational effort has also included both new ways to incorporate the polyelectrolyte character of DNA and other environmental forces in simulations of long chains and new methods to keep track of the multitude of configurations so generated. The collective advances are pointing to ways that will soon connect the sequences of base pairs in large genomes to folded three-dimensional structures based on natural bending, twisting and translational tendencies and in response to deformations produced by the binding of different proteins.

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 x 10(-19) dyne cm2, and persistence length, P = 500 A. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (delta l) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever delta l lies in the transition region. The free energies of the two minima are equal when delta lc = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be delta Gbar = (0.20) kBT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for delta l values in the transition region, and the two minimum mean potential energies are equal when delta l = 1.50. At the midpoint writhe, delta lc = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) kBT, and the difference in their entropies is 1.3 kB. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of delta l values from 0.85 to 1.85. The twist energy parameter (ET), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition.

Light scattering studies of supercoiled and nicked DNA

Static and dynamic light scattering measurements were made of solutions of pGem1a plasmids (3730 base pairs) in the relaxed circular (nicked) and supercoiled forms. The static structure factor and the spectrum of decay modes in the autocorrelation function were examined in order to determine the salient differences between the behaviors of nicked DNA and supercoiled DNA. The concentrations studied are within the dilute regime, which is to say that the structure and dynamics of an isolated DNA molecule were probed. Static light scattering measurements yielded estimates for the molecular weight M, second virial coefficient A2, and radius of gyration RG. For the nicked DNA, M = (2.8 +/- 0.4) x 10(6) g/mol, A2 = (0.9 +/- 0.2) x 10(-3) mol cm3/g2, and RG = 90 +/- 3 nm were obtained. For the supercoiled DNA, M = (2.5 +/- 0.4) x 10(6) g/mol, A2 = (1.2 +/- 0.2) x 10(-3) mol cm3/g2, and RG = 82 +/- 2.5 nm were obtained. The static structure factors for the nicked and supercoiled DNA were found to superpose when they were scaled by the radius of gyration. The intrinsic stiffness of DNA was evident in the static light scattering data. Homodyne intensity autocorrelation functions were collected for both DNAs at several angles, or scattering vectors. At the smallest scattering vectors the probe size was comparable to the longest intramolecular distance, while at the largest scattering vectors the probe size was smaller than the persistence length of the DNA. Values of the self-diffusion coefficients D were obtained from the low-angle data. For the DNA, D = (2.9 +/- 0.3) x 10(-8) cm2/s, and for the supercoiled DNA, D = (4.11 +/- 0.21) x 10(-8) cm2/s. The contribution to the correlation function from the internal dynamics of the DNA was seen to result in a strictly bimodal decay function. The rates of the faster mode gamma int, reached plateau values at low angles. For the nicked DNA, gamma int = 2500 +/- 500 s-1, and for the supercoiled DNA, gamma int = 5000 +/- 500 s-1. These rates correspond to the slowest internal relaxation modes of the DNAs. The dependence of the relaxation rates on scattering vector was monitored with the aid of cumulants analysis and compared with theoretical predictions for the semiflexible ring molecule. The internal mode rates and the dependence of the cumulants moments reflected the difference between the nicked DNA and the supercoiled DNA dynamical behavior. The supercoiled DNA behavior seen here indicates that conformational dynamics might play a larger role in DNA behavior than is suggested by the notion of a branched interwound structure.

Action at a distance in supercoiled DNA: effects of sequence on slither, branching, and intramolecular concentration

We report a computer modeling study of DNA supercoiling in model plasmids over the size range of 140-1260 bp. We used a computer model with basepair resolution. Molecular dynamics was used to produce ensembles at 300 K and to investigate intramolecular motions. The plasmid models varied by their sequence. The sequence types employed for comparison included a curve-bearing plasmid, a heterogenous sequence plasmid, and a homogenous sequence. Within the three sequence types tested at the 1260-bp plasmid size, we observed several sequence-dependent phenomena. Writhe, radius of gyration, slither motion, and branching probability were seen to be sequence dependent. Branching probability was the least in the homogenous plasmid and the greatest in the curve-bearing plasmid. The curve imposed a symmetry on the plasmid that was absent in the heterogenous sequence. Significant localizations and enhancements of intramolecular concentration were seen to a persistence length. Molecular dynamics allowed us to observe the mechanism of branch formation and reabsorption. We observed a size-dependent change in the types of motion observed in plasmids. Slither motion predominated in plasmids up to 600 bp in size, whereas global rearrangements were more important in the 1260 mer.

Flexing and folding double helical DNA

DNA base sequence, once thought to be interesting only as a carrier of the genetic blueprint, is now recognized as playing a structural role in modulating the biological activity of genes. Primary sequences of nucleic acid bases describe real three-dimensional structures with properties reflecting those structures. Moreover, the structures are base sequence dependent with individual residues adopting characteristic spatial forms. As a consequence, the double helix can fold into tertiary arrangements, although the deformation is much more gradual and spread over a larger molecular scale than in proteins. As part of an effort to understand how local structural irregularities are translated at the macromolecular level in DNA and recognized by proteins, a series of calculations probing the structure and properties of the double helix have been performed. By combining several computational techniques, complementary information as well as a series of built-in checks and balances for assessing the significance of the findings are obtained. The known sequence dependent bending, twisting, and translation of simple dimeric fragments have been incorporated into computer models of long open DNAs of varying length and chemical composition as well as in closed double helical circles and loops. The extent to which the double helix can be forced to bend and twist is monitored with newly parameterized base sequence dependent elastic energy potentials based on the observed configurations of adjacent base pairs in the B-DNA crystallographic literature.

Rigid-body motions of sub-units in DNA: a correlation analysis of a 200 ps molecular dynamics simulation

A 200 ps molecular dynamics simulation of the B-form double stranded self-complementary octanucleotide d(CTGATCAG) is analyzed in terms of correlated motions using the canonical analysis approach. Each nucleotide is decomposed in three sub-units corresponding to the base, the sugar ring and the backbone respectively. The correlation between the full dynamics of two sub-units was found to decrease as their mutual distance increases. The interpretation of the full dynamics of sub-units as the superimposition of rigid-body motions (translation and orientation) and deformation shows that the main source of correlation is rigid-body motions. Correlation between sub-units deformation is weak and practically vanishes for sub-units belonging to non-adjacent nucleotides. It is also shown that the correlation is much more important for sub-units of the same strand than of opposite strands. We conclude that the internal dynamics of the octanucleotide may be well described by rigid-body motions, the sub-units deformation having only local influence whereas sub-units translation and rotation have repercussion to long distances. The results presented in this study suggest how the number of degrees of freedom may be reduced for simulating long-time dynamics of oligonucleotides.

Modeling superhelical DNA: recent analytical and dynamic approaches

During the past year, a variety of diverse and complementary approaches have been presented for modeling superhelical DNA, offering new physical and biological insights into fundamental functional processes of DNA. Analytical approaches have probed deeper into the effects of entropy and thermal fluctuations on DNA structure and on various topological constraints induced by DNA-binding proteins. In tandem, new kinetic approaches--by molecular, Langevin and Brownian dynamics, as well as extensions of elastic-rod theory--have begun to offer dynamic information associated with supercoiling. Such dynamic approaches, along with other equilibrium studies, are refining the basic elastic-rod and polymer framework and incorporating more realistic treatments of salt and sequence-specific features. These collective advances in modeling large DNA molecules, in concert with technological innovations, are pointing to an exciting interplay between theory and experiment on the horizon.

Monte Carlo simulations of supercoiling free energies for unknotted and trefoil knotted DNAs

A new Monte Carlo (MC) algorithm is proposed for simulating inextensible circular chains with finite twisting and bending rigidity. This new algorithm samples the relevant Riemann volume elements in a uniform manner, when the constraining potential vanishes. Simulations are performed for filaments comprising 170 subunits, each containing approximately 28 bp, which corresponds to a DNA length of 4770 bp. The bending rigidity is chosen to yield a persistence length, P = 500 A, and the intersubunit potential is taken to be a hard-cylinder potential with diameter d = 50 A. This value of d yields the same second virial coefficient as the electrostatic potential obtained by numerical solution of the Poisson-Boltzmann equation for 150 mM salt. Simulations are performed for unknotted circles and also for trefoil knotted circles using two different values of the torsional rigidity, C = (2.0 and 3.0) x 10(-19) dyne cm2. In the case of unknotted circles, the simulated supercoiling free energy varies practically quadratically with linking difference delta l. The simulated twist energy parameter ET, its slope dET/dT, and the mean reduced writhe <w>/delta l for C = 3 x 10(-19) dyne cm2 all agree well with recent simulations for unknotted circles using the polygon-folding algorithm with identical P, d, and C. The simulated ET vs. delta l data for C = 2.0 x 10(-19) dyne cm2 agree rather well with recent experimental data for p30 delta DNA (4752 bp), for which the torsional rigidity, C = 2.07 x 10(-19) dyne cm2, was independently measured. The experimental data for p30 delta are enormously more likely to have arisen from C = 2.0 x 10(-19) than from C = 3.0 x 10(-19) dyne cm2. Serious problems with the reported experimental assessments of ET for pBR322 and their comparison with simulated data are noted. In the case of a trefoil knotted DNA, the simulated value, (ET)tre, exceeds that of the unknotted DNA, (ET)unk, by approximately equal to 1.40-fold at magnitude of delta l = 1.0, but declines to a plateau about 1.09-fold larger than (ET)unk when magnitude of delta l > or = 15. Although the predicted ratio, (ET)tre/(ET)unk approximately equal to 1.40, agrees fairly well with recent experimental measurements on a 5600-bp DNA, the individual measured ET values, like some of those reported for pBR322, are so large that they cannot be simulated using P = 500 A, d = 50 A, and any previous experimental estimate of C.

The influence of salt on the structure and energetics of supercoiled DNA

We present a detailed computational study of the influence of salt on the configurations, energies, and dynamics of supercoiled DNA. A potential function that includes both elastic and electrostatic energy components is employed. Specifically, the electrostatic term, with salt-dependent coefficients, is modeled after Stigter's pioneering work on the effective diameter of DNA as a function of salt concentration. Because an effective charge per unit length is used, the electrostatic formulation does not require explicit modeling of phosphates and can be used to study long DNAs at any desired resolution of charge. With explicit consideration of the electrostatic energy, an elastic bending constant corresponding to the nonelectrostatic part of the bending contribution to the persistence length is used. We show, for a series of salt concentrations ranging from 0.005 to 1.0 M sodium, how configurations and energies of supercoiled DNA (1000 and 3000 base pairs) change dramatically with the simulated salt environment. At high salt, the DNA adopts highly compact and bent interwound states, with the bending energy dominating over the other components, and the electrostatic energy playing a minor role in comparison to the bending and twisting terms. At low salt, the DNA supercoils are much more open and loosely interwound, and the electrostatic components are dominant. Over the range of three decades of salt examined, the electrostatic energy changes by a factor of 10. The buckling transition between the circle and figure-8 is highly sensitive to salt concentration: this transition is delayed as salt concentration decreases, with a particularly sharp increase below 0.1 M. For example, for a bending-to-twisting force constant ratio of A/C = 1.5, the linking number difference (delta LK) corresponding to equal energies for the circle and figure-8 increases from 2.1 to 3.25 as salt decreases from 1.0 to 0.005 M. We also present in detail a family of three-lobed supercoiled DNA configurations that are predicted by elasticity theory to be stable at low delta Lk. To our knowledge, such three-dimensional structures have not been previously presented in connection with DNA supercoiling. These branched forms have a higher bending energy than the corresponding interwound configurations at the same delta Lk but, especially at low salt, this bending energy difference is relatively small in comparison with the total energy, which is dominated by the electrostatic contributions. Significantly, the electrostatic energies of the three-lobed and (straight) interwound forms are comparable at each salt environment. We show how the three-lobed configurations change slowly with ALk, resulting in branched interwound forms at higher salt. In longer chains, the branched forms are highly interwound, with bent arms. At low salt, the branched supercoils are asymmetric, with a longer interwound stem and two shorter arms. From molecular dynamics simulations we observe differences in the motions of the DNA as a function of salt. At high salt, the supercoiled chain is quite compact but fairly rigid, whereas at low salt the DNA is loosely coiled but more dynamic. Especially notable at low salt are the large-scale opening and closing of the chain as a whole and the rapid "slithering"of individual residues past one another. Toroidal forms are not detected under these conditions. However, the overall features of the open, loose supercoils found at low salt are more similar to those of toroidal than interwound configurations. Indeed,simulated x-ray scattering profiles reveal the same trends observed experimentally and are consistent with a change from closed to open forms as salt is decreased. Like the minimization studies, the dynamics reveal a critical point near 0.1 M associated with the collapse of loose to tight supercoils. Near this physiological concentration, enhanced flexibility of the DNA is noted. The collective observations suggest a potential regulatory role for salt on supercoiled DNA function, not only for closed circular DNA,but also for linear DNA with small looped regions.